Obtaining analytic understanding in this type of interacting
systems is difficult, but at least the nature of the
instability leading to pattern formation and its relevant
spatial scale have been clarified by using partial
integro-differential equation descriptions of the mean field
type [1]}, [2]}, which are useful in
broader contexts [3]}, [4]}, [5]}.
However, from previous work in the Gaussian case
[6]}, [7]}, [8]}, it is known
that quantities such as cluster width and structure or
transition thresholds strongly depend on particle-number
fluctuations. Thus, obtaining additional results from
differential equation approaches would need the inclusion of
effective multiplicative noise terms [9]} or focus
on statistical quantities such as pair correlation functions
[10]}, [11]}, [12]}.
